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There has been a renewed controversy on the processes that determine evolution in spatially structured populations. Recent theoretical and empirical studies have suggested that parasites should be expected to be more “prudent” (less harmful and slower transmitting) when infection occurs locally. Using a novel approach based on spatial moment equations, we show that the evolution of parasites in spatially structured host populations is determined by the interplay of genetic and demographic spatial structuring, which in turn depends on the details of the ecological dynamics. This allows a detailed understanding of the roles of epidemiology, demography and network topology. Demographic turnover is needed for local interactions to select for prudence in the susceptible-infected models that have been the focus of previous studies. In diseases with little demographic turnover (as typical of many human diseases), we show that only parasites causing diseases with long-lived immunity are likely to be prudent in space. We further demonstrate why, at intermediate parasite dispersal, virulence can evolve to higher levels than predicted by non-spatial theory.

Intramolecular crosslinking is important in many processes, including nanoparticle fabrication, but quantitative models of the kinetics have not been extensively investigated. We propose a distribution kinetics analysis for simultaneous intramolecular and intermolecular crosslinking. For realistic cases, moment equations can be solved and crosslink density computed according to the number of crosslinks. An analytical solution for the ratio of intramolecular to intermolecular crosslinking rates varies inversely with the initial polymer concentration and initial molecular weight, in agreement with published experimental data.

A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description beyond the Navier-Stokes approximation. Various techniques, such as the method of partial summation, Pade approximants, and invariance principle are compared both in linear and nonlinear situations., Comment: 61 pages. Slightly edited and corrected version. It follows mostly Chapter 8 of the book: Gorban, A.N. and Karlin, I.V., Invariant Manifolds for Physical and Chemical Kinetics, Lect. Notes Phys. 660, Springer, Berlin, Heidelberg, 2005

The object of this work is to derive, based on a rigorous moment equations model, stricter explicit criteria for uniqueness and multiplicity of steady-states of isothermal CMSMPR crystallizers for both primary and secondary nucleation, as well as for size-dependent crystal growth rate. Regions in parameter space over which multiple steady states occur are derived, and the effects of the size-dependent crystal growth rate, of the rate of nucleation, and of the dilution of feed on the steady-state solutions are analyzed.

A kinetic model is presented for prediction of the gel properties in free-radical monovinyldivinyl monomer copolymerization. It is an extension of the kinetic model proposed recently for the sol species. The model involves the moment equations of the primary chains in the gel, and predicts the gel growth and structure as a function of the reaction time. Formulae for the chain length averages of the primary chains in the sol and in the gel were derived. The equations for calculating the number- and weight-average primary chain lengths are identical to the equations derived by statistical methods.

Grad-type approaches introduce an ansatz involving tensor Hermite functions with coefficients expresed in terms of moments of the ansatz. This formalism in usual form yields terms linear in first-order spatial derivatives in kinetic equations for the moments. Such terms disagree with alternative statistical derivations and phenomenological arguments. This disagreement is removed if different ansatzes are used to calculate entropy and moment equations. These are non-unique, and so Grad theory, while providing theoretical expressions for transport coefficients, does not serve uniquely to determine the structure of phenomenological equations.

A set of 21 moment fluid equations has been applied to two aspects relevant to scrape off layer plasma transport codes. The first of these is the provision of classical parallel transport coefficients, particularly for impurity plasma ions. Although more general results have been obtained, those only for a low impurity density common ion temperature plasma are presented. The results reflect the coupling between heat and particle fluxes and a coupling of the main ion fluxes into the impurity fluxes. The second application is in response to the problem of nonphysical values for classical viscosities and heat fluxes in regions with large gradients. The basic five moment description of the Braginskii equations has been extended to a full thirteen moment approximation. The new equations are given and some preliminary numerical results from a one dimensional code are discussed.

We developed an algorithm for simulating the effects of potential bag limits. The algorithm uses statistical distributions to model the frequency distribution of catch per trip. The moment equations of the distribution are keyed to stock abundance and the coefficient of fishing mortality rate, which allow the model to reflect the dynamics of the fishery. The catch with the bag limit is calculated by censoring the simulated distribution. We establish the conditions under which compounded Poisson distributions, such as the negative binomial, can be expected to provide adequate models for the catch distributions of recreational fisheries. We also discuss the assumptions that underlie the method of censoring catch-per-trip distributions, and, where appropriate, suggest alternative models. An example is developed in which we use the negative binomial distribution to model catch per trip and the familiar exponential model to simulate the change in stock abundance due to fishing mortality.

Moment equations offer an attractive framework for modeling non-equilibrium processes in moderately rarefied gases. We present a new hyperbolic closure for the 5-moment system in the one-dimensional setting that couples the conservation laws of mass, momentum and energy to two evolution equations of higher, non-equilibrium moments. The new closure, given in closed-form, depends on a regularization parameter β that is related to the non-linearity around the equilibrium state, so as to mitigate the appearing sub-shock in the continuous shock-structure problem. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper demonstrates the application of the theory of temperature multiplicity to the continuous mixed-suspension, mixed-product removal (MSMPR) cooling crystallizer as described by the coupled solute and energy balances along with the associated population balance transformed into moment equations. Exact uniqueness and multiplicity criteria are developed. Applications to specific cases together with diagrams depicting the effects of the important variables on the regions of multiplicity and uniqueness are presented.

Ziel der Untersuchung ist, den Verlauf der Stromungsgrosen und den Grad der Dissoziation in starken Stoswellen (Ma > 25) durch zweiatomige Gase zu bestimmen. Dabei wird angenommen, das wegen der besonders energiereichen Teilchenstose Molekule aus dem Grundzustand der Vibration dissoziieren konnen, bevor Translationsgleichgewicht erreicht ist. Auserdem soll die Verteilungsfunktion aus einer Linearkombination der Gleichgewichtsverteilungen vor und nach der Stosfront bestehen. Um das Problem beschreiben zu konnen, benotigt man neben den Erhaltungsgleichungen eine hohere Momentengleichung. Um den Einflus des Exponenten der Molekuleigenschaft abschatzen zu konnen, werden verschiedene Momentengleichungen aufgestellt. Zur Beschreibung der chemischen Prozesse in der Stosfront ist eine zusatzliche Gleichung erforderlich. Die darin auftretenden Ratenkonstanten wurden aus gemessenen Werten fur den sehr hohen Temperaturbereich am Ende der Stosfront extrapoliert. Gleichzeitig wurde aus theoretischen Uberlegungen ein statistischer Ratenkoeffizient abgeleitet, welcher die verschiedenen Temperaturen der stosenden Teilchen berucksichtigt. Das nichtlineare Differentialgleichungssystem wird numerisch integriert. Dabei wird ein implizites Verfahren verwendet, welches bei vertretbarer Rechenzeit genugend Genauigkeit ergibt. Die Ergebnisse stimmen mit dem erwarteten Verlauf der Stromungsgrosen und dem Dissoziationsgrad uberein. Es zeigt sich, das bei Verwendung der theoretischen Ratenkonstante bei der Machzahl Ma = 50 alle Molekule am Ende der Stosfront dissoziiert sind. Neben diesen Ergebnissen wird der Einflus der Molekuleigenschaft auf die Stromungsgrosen diskutiert. The present investigation analyses the dependence of physical variables including the degree of dissociation past strong shock waves (M > 25) through diatomic gases. The calculations assume dissociation from the vibrational ground state before translational equilibrium can be established, an assumption which is possible because of the high relative kinetic energy. It is assumed that the distribution function is a linear combination of distribution functions in the equilibrium state before and behind the shock front. For the set of the equations defining the system one needs besides the conservation equations one more higher moment equation. To estimate the influence of the exponent of the molecular property, several moment equations are formed. An additional equation is required for the chemical reactions within the shock front. The necessary rate-constants have been extrapolated from measured values to the extreme temperatures occurring at the end of the shock front. In addition, a statistical rate-coefficient is derived from theoretical considerations which takes into account the different temperatures of the colliding particles. The resulting system of nonlinear differential equations is integrated numerically by means of an implicit technique which gives sufficient accuracy with economic integration time. The results agree with the expected values of the flow variables and the degree of dissociation. It turns out that all molecules have been dissociated at the end of the shock front if the theoretical rate constants are applied to shocks of M = 50. In addition to the discussion of these results, the influence of the molecular properties on the flow variables is discussed.

In solidification, one is primarily interested in the movement of the solid-liquid interface and not in the details of the internal temperature distribution. This is parallelled in many other processes of practical interest. Because of the linearity of the governing equation, one may readily obtain an integral relationship between the system variables, as expressed by the moment equations. By further introducing physically reasonable assumptions, one obtains bounding or approximate solutions, some of which are simple but accurate analytic expressions.